Each week a certain salesman is paid a fixed amount equal to

For your what if scenario the answer is as follows -

Amount from the commission would be 0 and salesman would have made last week only $300. Typically in GMAT you take the question and statements as facts.

//kudos please, if the above explanation is good.

In a data sufficiency question is it necessary for both the statements to return the same unique value ?
I was going through another post of the same question , in which PiyushK has provided a new statement :modified statement 1 : Sales man income was 50% of his total sale.
The below is the link to the question-
each-week-a-certain-salesman-is-paid-a-fixed-amount-equal-to-6616.html

Experts please help!!

Yes, both the statements are a part of the same question. One cannot return that x is 2 if the other says that x is 7. In one question, x can take only one unique value.
So if both statements are giving you a unique value, the value will be the same. If it isn't, it means you have made a mistake somewhere.
Of course, it is possible that one statement gives you a bunch of possible values for x and the other gives you a unique value but obviously, the unique value would be a part of the bunch of values given by the other statement.

Thanks a lot VeritasPrepKarishma

"Of course, it is possible that one statement gives you a bunch of possible values for x and the other gives you a unique value but obviously, the unique value would be a part of the bunch of values given by the other statement"
As per this if statement 1 returns 2 values of x - a and b
and statement 2 returns a single value of x = a
Then we can conclude that x=a is the solution.
Then our answer choice will be C right ?
In other words x can take a value which is intersection of result set 1 and 2 .
And if the intersection of the 2 result sets is null then we will have option E .

So this is why DS questions are tricky. Think about it:

if statement 1 returns 2 values of x - a and b
and statement 2 returns a single value of x = a
Then we can conclude that x=a is the solution.

Correct!

Then our answer choice will be C right ?

Wrong! The answer will be (B) in that case (assuming statement II tells you that x = a). If one statement gives you a unique value for x, it alone is sufficient. We don't need the more generic other statement which gives us multiple values for x.

When will the answer be (C)?
When statement 1 gives x = a or b and statement 2 gives x = a or c
Now you need both statements to see that x can take only one value "a", if it has to satisfy both statements.

And if the intersection of the 2 result sets is null then we will have option E .
If intersection of the two result sets in null, it is a wrong DS question since there has to be at least one common value (your original question). The answer will be (E) when the two sets have multiple values in the overlap.
When statement 1 gives x = a or b or c and statement 2 gives x = a or c.
Using both statements, we can say that x is either a or c. But we do not know which. So answer is (E)

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5 percent of the amount of his sales that week over $1,000. What is the total amount the salesman was paid last week?

(1) The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week.
(2) The salesman's sales last week totaled $5,000.

If we modify the question, making sales' payment:p, sales amount:s, p=300+(s-1000)5%. There are 2 variables (p,s) and an equation, so we need one more equation when 2 are actually given from the 2 conditions; there is high chance (D) will be our answer.
From condition 1, it is sufficient as p=0.1s
and condition 2 is also sufficient in s=5000. The answer therefore becomes (D)

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

Hi all,

I'm a fresh GMATer. for this question, I have only one question(but I think it won't affect the answer)

when his sales > 1000, the commission should be 5%*S. Because I think 1000 is not a value, just a precondition.

I don't know whether my understanding is right or not...

Please read this: https://gmatclub.com/forum/each-week-a- ... l#p1106484

Say S is the amount of his sales that week, then:

If \(S\leq{1,000}\), salesman's profit is \($300\);
If \(S>1,000\), salesman's profit is \($300+(S-1,000)*0.05\).

Why we need to minus 1,000, 0.05*(S-1,000) instead of 0.05*S ?

For example Sales = 2,000, Commission = 0.05*2,000

No.

Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5 percent of the amount of his sales that week OVER $1,000. What is the total amount the salesman was paid last week?

So, if S = 2,000, then commission = (2,000 - 1,000)*0.05 and the profit = 300 + (2,000 - 1,000)*0.05.

Hope it's clear.

Given: Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5 percent of the amount of his sales that week over $1,000.
Let T = Total sales last week
So (T - 1000) = the amount that EXCEEDS $1000
Total paycheck = $300 + 5% of (T - 1000)
Or we can write: Total paycheck last week = $300 + 0.05(T - 1000)

Target question: What is the total amount the salesman was paid last week?

Statement 1: The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week.
We can write: 300 + 0.05(T - 1000) = 10% of T
In other words, 300 + 0.05(T - 1000) = 0.1T

ASIDE: at this point, we should recognize that we COULD solve the above equation for T, which means we COULD determine how much the salesman was paid last week.
So, statement 1 is SUFFICIENT.

That said, let's solve the equation (for "fun")
Take: 300 + 0.05(T - 1000) = 0.1T
Simplify: 300 + 0.05T - 50 = 0.1T
Simplify: 250 + 0.05T = 0.1T
Subtract 0.05T from both sides: 250 = 0.05T
Solve: T = 5000
If T = 5000, then: Total paycheck last week = $300 + 0.05(5000 - 1000)
= 300 + 0.05(4000)
= 300 + 200
= 500
So, the answer to the target question is $500
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The salesman's sales last week totaled $5,000
In other words, T = 5000
Total paycheck last week = $300 + 0.05(5000 - 1000)
= 300 + 0.05(4000)
= 300 + 200
= 500
So, the answer to the target question is $500
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

Answer: Option D

Video solution by GMATinsight



Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub

Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1

Classic question from the official source mba.com

Hi Bunuel KarishmaB chetan2u
Reading the question, I understood the commission as the sum of sales that are over 1000. For e.g. If total sales are 4000 split into 1 sale of 2000 and 4 sales of 500 then commission would be 5% of 2000 not 5% of 3000.

Can you help me with where I am going wrong?

Ps. I understood the logic in the answer posts but I think I'm wrong in understanding the language of the question.

Here, Sales = Revenue
"amount of revenue" makes perfect sense.

If Sales were meant to be transactions, we would have been given "5% of those sales that brought in more than $1000 each" etc. There is no discussion of the number of transactions etc. Usually, sales will mean revenue.

Bunuel KarishmaB JeffTargetTestPrep

I have a simple doubt, the question here asks us What is the total amount the salesman was paid last week? which means we have to find if we can find the exact numerical answer of the given question and not If we can find the data or not as this is not a Yes/No question

So by this logic we can use Statement 2 to get exact numeric value and using Statement 1 we get an equation and not exact numeric value, considering all these facts the shouldn't the answer be Option B instead of D ?